What do the following two equations represent? $-x-4y = 2$ $-x-4y = -4$
Solution: Putting the first equation in $y = mx + b$ form gives: $-x-4y = 2$ $-4y = x+2$ $y = -\dfrac{1}{4}x - \dfrac{1}{2}$ Putting the second equation in $y = mx + b$ form gives: $-x-4y = -4$ $-4y = x-4$ $y = -\dfrac{1}{4}x + 1$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.